1. ## prime numbers

Hi

Something i've noticed about prime numbers. If you multiply consecutive prime numbers i.e. 2x3x5=30
and then add the other consecutive primes you get a prime or a prime x prime.

30+7= 37
30+11=41
30+13=43
30+17=47
30+19= 49 (7x7)

Phil

2. ## Re: prime numbers

17*19 + 23 + 29 = 375 which is 5*5*5*3

3. ## Re: prime numbers

I used python to test this out and it quickly became unwieldy, although I managed to get some results.

Multiplying consecutive primes starting from 2 and adding the last consecutive prime.
Code:
6 + 5 = 11     is prime
30 + 7 = 37     is prime
210 + 11 = 221     13 * 17
2310 + 13 = 2323     23 * 101
30030 + 17 = 30047     is prime
510510 + 19 = 510529     is prime
9699690 + 23 = 9699713     is prime
223092870 + 29 = 223092899     127 * 1231 * 1427    False
6469693230 + 31 = 6469693261     107 * 787 * 76829    False
Multiplying consecutive primes and then adding any greater prime.
Code:
2x3 = 6
6 + 5 = 11  ->  is prime
6 + 7 = 13  ->  is prime
6 + 11 = 17  ->  is prime
6 + 13 = 19  ->  is prime
6 + 17 = 23  ->  is prime

2x3x5 = 30
30 + 7 = 37  ->  is prime
30 + 11 = 41  ->  is prime
30 + 13 = 43  ->  is prime
30 + 17 = 47  ->  is prime
30 + 19 = 49  ->  7 * 7

2x3x5x7 = 210
210 + 11 = 221  ->  13 * 17
210 + 13 = 223  ->  is prime
210 + 17 = 227  ->  is prime
210 + 19 = 229  ->  is prime
210 + 23 = 233  ->  is prime

2x3x5x7x11 = 2310
2310 + 13 = 2323  ->  23 * 101
2310 + 17 = 2327  ->  13 * 179
2310 + 19 = 2329  ->  17 * 137
2310 + 23 = 2333  ->  is prime
2310 + 29 = 2339  ->  is prime

2x3x5x7x11x13 = 30030
30030 + 17 = 30047  ->  is prime
30030 + 19 = 30049  ->  151 * 199
30030 + 23 = 30053  ->  41 * 733
30030 + 29 = 30059  ->  is prime
30030 + 31 = 30061  ->  23 * 1307

2x3x5x7x11x13x17 = 510510
510510 + 19 = 510529  ->  is prime
510510 + 23 = 510533  ->  83 * 6151
510510 + 29 = 510539  ->  31 * 43 * 383    False
510510 + 31 = 510541  ->  307 * 1663
510510 + 37 = 510547  ->  139 * 3673

2x3x5x7x11x13x17x19 = 9699690
9699690 + 23 = 9699713  ->  is prime
9699690 + 29 = 9699719  ->  47 * 47 * 4391    False
9699690 + 31 = 9699721  ->  23 * 421727
9699690 + 37 = 9699727  ->  is prime
9699690 + 41 = 9699731  ->  is prime

2x3x5x7x11x13x17x19x23 = 223092870
223092870 + 29 = 223092899  ->  127 * 1231 * 1427    False
223092870 + 31 = 223092901  ->  43 * 5188207
223092870 + 37 = 223092907  ->  is prime
223092870 + 41 = 223092911  ->  29 * 29 * 265271    False
223092870 + 43 = 223092913  ->  6971 * 32003
I thought I might as well post it.

Could only find 6 occurrences where this was False. This is a small sample, but I think you were on to something, at least for a quick way of finding a number which is likely prime or semi-prime.